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                Claris的剑                </h1>
                <p>时间限制：10s&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;  空间限制：256MB</p>			</div>
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                                <h3>题目描述</h3><p><p>Claris想要铸一把剑，这把剑必须符合他的审美，具体来说，我们可以把这把剑的不同地方的宽度看成一个序列，这个序列要满足以下条件：<br />
1.每个元素都是正整数（你的宽度不可能是负数吧）<br />
2.每个元素不能超过M，太宽了如果比Claris身高还高怎么办（你可以认为Claris的身高就是M）<br />
3.相邻两个元素的差的绝对值必须是1（如果是0，则这个地方不是锯齿，杀伤力不够，如果太大，又太丑了）<br />
4.第一个元素的值必须是1（剑尖必须是最窄的地方）<br />
他想知道有多少把长度不超过N（即宽度的序列长度不超过N）的合法的本质不同的剑。<br />
我们认为两把剑本质不同，当且仅当存在至少一个宽度，在两把剑的宽度序列里面出现次数不一样。<br />
比如{1,2,3}和{1,3,2}是本质相同的<br />
{1,2,3}和{1,2,1}则是本质不同的</p></p><hr/><h3>输入格式</h3><p><p>只有两个整数，表示N,M (数据保证$N,M \leq 2000000$)</p></p><hr/><h3>输出格式</h3><p><p>只有一个整数，表示答案对$10^9+7$取模的结果</p></p><hr/><h3>样例输入</h3><pre>5 3</pre><hr/><h3>样例输出</h3><pre>9</pre><hr/><h3>提示</h3><p><p>样例解释<br />
<br />
所有本质不同的合法的剑有如下：<br />
<br />
{1}<br />
{1,2}<br />
{1,2,3}<br />
{1,2,1}<br />
{1,2,3,2}<br />
{1,2,1,2}<br />
{1,2,3,2,3}<br />
{1,2,3,2,1}<br />
{1,2,1,2,1}</p></p><hr/><h3>题目来源</h3><p>By lyzy</p>
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